Are there faster ways to switch pose modes? Am I missing something?
Personally when I do weight painting (or any rigged mesh work really), I split and pin the Pose/Rest controls in their own pane at the far bottom right, with bone layers and IK toggles in the same pin. That way it's just a single click to get to rest pose and back no matter what objects I have selected.
In addition, this workflow might help out a bit:

Object Mode
Select Rig
Shift-select Mesh object(s)
Weight Paint Mode.

This should allow you to select any bone in weight paint mode, pose them and paint the related vertex weights in real time, with the armature panel pinned it makes it a lot easier to do operations that require rest pose.